Question

In each case, determine the value of the constant c that makes the probability statement correct. (Round your answers to two decimal places.)

(a)    Φ(c) = 0.9821


(b)    P(0 ≤ Z ≤ c) = 0.3051


(c)    P(c ≤ Z) = 0.1314


(d)    P(−c ≤ Z ≤ c) = 0.6528


(e)    P(c ≤ |Z|) = 0.0128

Answer 1

Solution

Given that,

Using standard normal table,

a ) = 0.9821

P(Z < z) = 0.9821

P(Z < 2.099) = 0.9821

c = 2.10

b ) P( 0 z c) = 0.3051

P(Z c) - P(Z 0) = 0.3051

P(Z c) = P(Z 0) + 0.3051

P(Z c) = 0.5 + 0.3051 = 0.8051

P(Z 0.86) = 0.8051

c = 0.86

c ) P(c Z) = 0.1314

P(Z c) =0.1314

1 - P(Z c) = 0.1314

P(Z c) = 1 - 0.1314 = 0.8643

P(Z 1.12) = 0.8686

c = 1.12

d ) P(-c Z c) = 0.6528

P(Z c) - P(Z -c) = 0.6528

2P(Z c) - 1 = 0.6528

2P(Z c) = 1 + 0.6528 = 1.6528

P(Z c) = 1.6528 / 2 = 0.8264

P(Z 0.94) = 0.8264

c = 0.94

e ) P(c |Z|) = 0.0128

2 * [1 - P(z < c)] = 0.0128

1 - P(z < c) = 0.0128 / 2 = 0.0064

P(z < c) = 1 - 0.0064 = 0.9936

P(z < 2.49) = 0.9936

c = 2.49